Search

Let A be an expanding matrix with characteristic polynomial $$f(x)=x^2+px+3$$ and $$\mathcal {D}=\{0,v,\ell v+kAv\}$$ be a digit set where $$\ell ,k\in {\mathbb {Z}},\ v\in {\mathbb {R}}^2$$ so that $$\{v,Av\}$$ is linearly independent. It is well known that there exists a unique self-affine fractal T satisfying $$AT=T+\mathcal {D}$$ . In this paper, we give a complete characterization for the connectedness of T by using radix expansion.